Answer:
[tex]\boxed{\sf distance \: between \: the \: objects \: \: is \: 2.5 \: cm}[/tex]
Step-by-step explanation:
According to universal law of gravitation every object in the universe attracts every other particles that surrounds it with a force which is inversely proportional to the square of their distance of separation & directly proportional to
the product of their masses, given by standard formula.
[tex]A = G \cdot \frac{m_1.m_2}{ {d}^{2} } [/tex]
where A,d & G are force of attraction, distance of separation & proportionality constant respectively.
Given:
A1 = 2 units
d1= 5 cm
A2 = 8 units
To find:
Distance of separation when the force of attraction is 8 units d2 = ?
Solution:
Substituting the given values in above at each point,
[tex]A_1 = G \cdot \frac{m_1.m_2}{ {d_1}^{2} } \\ 2 = G \cdot \frac{m_1.m_2}{ {5}^{2} } \\ \sf similarly \: at \: second \: point \: of \: attraction \\ A_2 = G \cdot \frac{m_1.m_2}{ {d_2}^{2} } \\ 8 = G \cdot \frac{m_1.m_2}{ {d_2}^{2} } \\ \sf \: \: dividing \: both \: of \: the \: equation \\ \frac{2}{8} = \frac{G \cdot \frac{m_1.m_2}{ {5}^{2} }}{G \cdot \frac{m_1.m_2}{ {d_2}^{2} } } \\ \sf \: G \: m_1 and \: m_2 \: are \: \: constant \: hence \\ \sf they \: can \: be \: cancelled \: out \\ \frac{2}{8} = \frac{ \frac{1}{ {5}^{2} } }{ \frac{1}{ {d_2}^{2} } } \\ \sf rearranging \: above \: equation \\ \frac{1}{4} = \frac{{d_2}^{2} }{ {5}^{2} } \\ {d_2}^{2} = \frac{ {5}^{2} }{4 } \\ {d_2}^{2} = \frac{25}{4} \\ {d_2}^{2} = 6.25 \\ \sqrt{{d_2}^{2} } = \sqrt{6.25} \\ \boxed{ \sf{d_2} = 2.5 \: cm}[/tex]
Answer: the distance between the two objects is 2.5 cm, if the attraction between them is 8 units.
Learn more about universal law of gravitation here https://brainly.com/question/27244479
Thanks for joining brainly community!
